The area of a circle is the amount of space inside the circle. Area is always written as units squared (in², cm²). A formula is an equation that declares.

Presentation on theme: "The area of a circle is the amount of space inside the circle. Area is always written as units squared (in², cm²). A formula is an equation that declares."— Presentation transcript:

The area of a circle is the amount of space inside the circle. Area is always written as units squared (in², cm²). A formula is an equation that declares the relationship between two or more quantities. Pi (  ) also used in the formula to find the area of a circle. What is the formula for using radius to find the area of a circle? In your own words, what is the area of a circle? “The area of a circle is _____________.” CFU 1 2 a number that does not change Vocabulary Lesson 3.16.15 Introduction   3.14 How is radius related to diameter? In your own words, the radius is exactly ________ of the diameter. CFU 2 Using the radius (r) area radius diameter A round carpet disc has a radius of 3 ft. The rug takes up 28.26 ft² of space. Area Formula: 3 ft What can you do if you only know the diameter of the circle, but you want to find the area of the circle? CFU 3

Area (Pair-Share) What do you think the difference is between the CIRCUMFERENCE of a circle and the AREA of a circle? CFU

The circumference of a circle is the distance around the circle. The area of a circle is the space inside the circle. A formula is an equation that declares the relationship between two or more quantities. Pi (  ) is the constant 1 ratio of the circumference to the diameter of a circle. Chan is creating a circular garden. For which will he need to find the circumference? How do you know? A Chan wants to build a fence around the garden. B Chan wants to add soil to cover the garden. In your own words, what is the circumference of a circle? “The circumference of a circle is _____.” CFU 1 Circumference 1 a number that does not change Vocabulary Concept Development (Continued) Area 4 feet A rug has a radius of 4 feet.   3.14 C = 2  r   A =   r 2 Chan is creating a circular garden. For which situation will he need to find the area? How do you know? A Chan wants to build a fence around the garden. B Chan wants to add soil to cover the garden. In your own words, what is the area of a circle? “The area of a circle is _____.” CFU 2 Animated

1.A cookie has a diameter of 8 centimeters. What is the circumference of the cookie? The circumference of a circle is the distance around the circle. Pi (  ) is the constant ratio of the circumference to the diameter of a circle. 2 find (synonym) 3 figure out Vocabulary Skill Development/Guided Practice C = 2  r   C = 2  4   C = 8  3.14 C = 25.12 “The circumference of the cookie is 25.12 centimeters.”   3.14 Circumference C = 2  r   Area A =   r 2 Read the problem carefully. Identify 2 the given information. (underline) Determine 3 which formula to use. Substitute the given information into the formula and solve. Interpret the answer. (sketch and explain) Solve problems for the area and circumference of a circle. 1 2 3 a b How did I/you identify the given information? How did I/you determine which formula to use? How did I/you interpret the answer? CFU 3 1a 1b

2.A junior (kid’s) basketball hoop has a diameter of 10 inches. What is the circumference of the basketball hoop? The circumference of a circle is the distance around the circle. Pi (  ) is the constant ratio of the circumference to the diameter of a circle. 2 find (synonym) 3 figure out Vocabulary Skill Development/Guided Practice (continued) C = 2  r   C = 2  5   C = 10  3.14 C = 31.4 “The circumference of the hoop is 31.4 inches.”   3.14 Circumference C = 2  r   Area A =   r 2 Read the problem carefully. Identify 2 the given information. (underline) Determine 3 which formula to use. Substitute the given information into the formula and solve. Interpret the answer. (sketch and explain) Solve problems for the area and circumference of a circle. 1 2 3 a b How did I/you identify the given information? How did I/you determine which formula to use? How did I/you interpret the answer? CFU 3 1a 1b

3.A BMX bicycle wheel has a radius of 10 inches. How far will the wheel travel each time it turns? Skill Development/Guided Practice (continued) C = 2  r   C = 2  10   C = 20  3.14 C = 62.80 The circumference of a circle is the distance around the circle. Pi (  ) is the constant ratio of the circumference to the diameter of a circle.   3.14 Circumference C = 2  r   Area A =   r 2 Read the problem carefully. Identify the given information. (underline) Determine which formula to use. Substitute the given information into the formula and solve. Interpret the answer. (sketch and explain) Solve problems for the area and circumference of a circle. 1 2 3 a b How did I/you identify the given information? How did I/you determine which formula to use? How did I/you interpret the answer? CFU 3 1a 1b “The wheel will travel 62.80 inches each time it turns one full turn around.”

4.A personal sized pizza has a radius of 6 inches. How long is the crust around the pizza? Skill Development/Guided Practice (continued) C = 2  r   C = 2  6   C = 12  3.14 C = 37.68 “The crust is 37.68 inches long.” The circumference of a circle is the distance around the circle. Pi (  ) is the constant ratio of the circumference to the diameter of a circle.   3.14 Circumference C = 2  r   Area A =   r 2 Read the problem carefully. Identify the given information. (underline) Determine which formula to use. Substitute the given information into the formula and solve. Interpret the answer. (sketch and explain) Solve problems for the area and circumference of a circle. 1 2 3 a b How did I/you identify the given information? How did I/you determine which formula to use? How did I/you interpret the answer? CFU 3 1a 1b

5.A barrel has a radius of 12 inches. What is the area of the top of the barrel? 6.A pie has a radius of 7 centimeters. What is the area of the top of the pie? Skill Development/Guided Practice 2 A =   r 2 A =   12 2 A = 3.14  144 A = 452.16 “The area of the top of the barrel is 452.16 square inches.” A =   r 2 A =   7 2 A = 3.14  49 A = 153.86 “The area of the top of the pie is 153.86 square centimeters.” The area of a circle is the space inside the circle. Pi (  ) is the constant ratio of the circumference to the diameter of a circle.   3.14 Circumference C = 2  r   Area A =   r 2 Read the problem carefully. Identify the given information. (underline) Determine which formula to use. Substitute the given information into the formula and solve. Interpret the answer. (sketch and explain) Solve problems for the area and circumference of a circle. 1 2 3 a b How did I/you identify the given information? How did I/you determine which formula to use? How did I/you interpret the answer? CFU 3 1a 1b Skill Development/Guided Practice (continued)

7.An X-Large Lucia’s pizza has a diameter of 18 inches. How much space will be on top for toppings? 8.A round dining table has a diameter of 6 feet. How much cloth is needed to make a tablecloth? Skill Development/Guided Practice (continued) A =   r 2 A =   9 2 A = 3.14  81 A = 254.34 “The top of the pizza has 254.34 square inches for toppings.” A =   r 2 A =   3 2 A = 3.14  9 A = 28.26 “28.26 square feet of cloth is needed to make a tablecloth.” Read the problem carefully. Identify the given information. (underline) Determine which formula to use. Substitute the given information into the formula and solve. Interpret the answer. (sketch and explain) Solve problems for the area and circumference of a circle. 1 2 3 a b The area of a circle is the space inside the circle. Pi (  ) is the constant ratio of the circumference to the diameter of a circle. How did I/you identify the given information? How did I/you determine which formula to use? How did I/you interpret the answer? CFU 3 1a 1b   3.14 Circumference C = 2  r   Area A =   r 2

9.Ephraim wants to make a round garden 6 feet across. How much fencing will he need to go around the outside? How much ground will he need to cover in fertilizer? 10.Mr. Garcia is building a circular stage that has a radius of 9 feet. How much planking will it take to cover the stage? The cast would like to cover the edge of the stage with garland. How long will it have to be to go all the way around? A =   r 2 A =   3 2 A = 3.14  9 A = 28.26 C = 2  r   C = 2  3   C = 6   C = 18.84 “He will have to cover 28.26 square feet with fertilizer.” A =   r 2 A =   9 2 A = 3.14  81 A = 254.34 How did I/you determine what the question is asking? How did I/you determine the math concept required? How did I/you determine the relevant information? How did I/you solve and interpret the problem? How did I/you check the reasonableness of the answer? CFU 2 1 3 4 5 Skill Development/Guided Practice (continued) “Mr. Garcia will need 254.34 square feet of planking to cover the stage.” “Ephraim will need 18.84 feet of fencing.” C = 2  r   C = 2  9   C = 18   C = 56.52 “The cast will need 56.52 feet of garland to go around the stage.”

1.A mirror has a radius of 5 centimeters. How long will the frame have to be to go around the mirror? 2.What is the area of the mirror? What did you learn today about solving problems for the area and circumference of a circle? (Pair-Share) Use words from the word bank. Access Common Core Summary Closure Word Bank circumference area circle pi (  ) radius diameter Gary is replacing the leather cover on a stool. What measurement could he find so that the new leather cover is the same size as the old one? How do you know? C = 2  r   C = 2  5   C = 10   C = 31.4 “The frame will have to be 31.4 centimeters long.” A =   r 2 A =   5 2 A =   25 A = 78.5 “The mirror has an area of 78.5 square centimeters.” Read the problem carefully. Identify the given information. (underline) Determine which formula to use. Substitute the given information into the formula and solve. Interpret the answer. (sketch and explain) Solve problems for the area and circumference of a circle. 1 2 3 a b Skill Closure The circumference of a circle is the distance around the circle. The area of a circle is the space inside the circle. Pi (  ) is the constant ratio of the circumference to the diameter of a circle.   3.14 Circumference Area A =   r 2 C = 2  r   OR C = d  

1.A platter has a diameter of 14 inches. What is the circumference of the platter? 2.A round pool has a radius of 14 feet. How long is the edge around the pool? Independent Practice C = 2  r   C = 2  7   C = 14  3.14 C = 43.96 “The circumference of the platter is 43.96 inches.” C = 2  r   C = 2  14   C = 28  3.14 C = 87.92 “The edge around the pool is 87.92 feet long.” The circumference of a circle is the distance around the circle. The area of a circle is the space inside the circle. Pi (  ) is the constant ratio of the circumference to the diameter of a circle. Read the problem carefully. Identify the given information. (underline) Determine which formula to use. Substitute the given information into the formula and solve. Interpret the answer. (sketch and explain) Solve problems for the area and circumference of a circle. 1 2 3 a b Circumference C = 2  r   Area A =   r 2   3.14

3.A tree stump has a radius of 24 inches. How much area is on top of the stump? 4.James is replacing a stool top that has a radius of 13 centimeters. How much wood is needed to make a new top? Independent Practice (continued) A =   r 2 A =   24 2 A = 3.14  576 A = 1,808.64 “The top of the stump measures 1,808.64 square inches.” A =   r 2 A =   13 2 A = 3.14  169 A = 530.66 “The top of the stool will need 530.66 square centimeters of wood.” The circumference of a circle is the distance around the circle. The area of a circle is the space inside the circle. Pi (  ) is the constant ratio of the circumference to the diameter of a circle. Read the problem carefully. Identify the given information. (underline) Determine which formula to use. Substitute the given information into the formula and solve. Interpret the answer. (sketch and explain) Solve problems for the area and circumference of a circle. 1 2 3 a b Circumference C = 2  r   Area A =   r 2   3.14

5.A round patch of grass is 48 feet across. How much area does the patch cover? How long would a fence around the grass be? 6.An oil pipeline has a radius of 12 inches. How long must each bracket be to go around the pipe and hold it up? How large is the cap on the end of the pipe? Independent Practice (continued) A =   r 2 A =   24 2 A = 3.14  576 A = 1,808.64 C = 2  r   C = 2  24   C = 48   C = 150.72 “A fence to go around the patch would be 150.72 feet long.” A =   r 2 A =   12 2 A = 3.14  144 A = 452.16 C = 2  r   C = 2  12   C = 24   C = 75.36 “The end caps are 452.16 square inches.” “The patch of grass covers 1,808.64 square feet.” “The brackets must reach 75.36 inches around the pipeline.”

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